I recently got Damn Small Linux running inside Virtual Box on Linux Mint. I was wondering if there was any way to let people connect to one of my DSL virtual machines through their web browsers from their computers across the internet. If it's not possible with virtual box, I would be open to switching to another virtualization solution, such as VMWare. Thanks!
It should not be a problem.
First, I assume you mean "connect with a webbrowser to a webserver" and you have a webserver up and running on your virtual DSL-machine.
By default, VirtualBox has it's own internal network where all VMs get ip-addresses like in a NAT. In the VirtualBox "main window", select your DSL VM and go to settings. In network settings, set the connection to "bridged". Now your VM is listening on the same NIC as your Linux Mint host.
By setting an appropiate IP-address for your DSL VM (one that fits your local network), you should now be able to access the VM from your own host or anywhere else in your local network.
Assuming you are running your host behind a NAT, you will now have to edit your router settings, so the web requests are going to your VM.